## Stores all the few-shot examples

# Few-shot examples for concept decomposition
CONCEPT_DECOMPOSITION_EXAMPLES_1= {
  "main_concept": "Algebra",
  "Explanation": "Algebra is a branch of mathematics that uses symbols and letters to represent numbers and their relationships. It helps solve equations and understand patterns.",
  "sub_concepts": [
    {
      "id": "1.1",
      "name": "Functions",
      "description": "Functions show how one quantity depends on another and are used to model relationships.",
      "difficulty": "basic"
    },
    {
      "id": "1.2",
      "name": "The Domain and Range of a Function",
      "description": "Domain is the set of input values, and range is the set of output values for a function.",
      "difficulty": "basic"
    },
    {
      "id": "1.3",
      "name": "Intervals and Interval Notation",
      "description": "A way to write ranges of values between two endpoints.",
      "difficulty": "basic"
    },
    {
      "id": "1.4",
      "name": "Even and Odd Functions",
      "description": "Even functions are symmetrical about the y-axis; odd functions are symmetrical about the origin.",
      "difficulty": "intermediate"
    },
    {
      "id": "1.5",
      "name": "Function Graph Transformations: Vertical and Horizontal Shifts",
      "description": "Moves the graph of a function up, down, left, or right.",
      "difficulty": "intermediate"
    },
    {
      "id": "1.6",
      "name": "Function Graph Transformations: Stretching, Reflecting, and Compressing",
      "description": "Changes the shape of a graph by stretching, flipping, or squeezing it.",
      "difficulty": "intermediate"
    },
    {
      "id": "1.7",
      "name": "Function Graphs: Combined Transformations",
      "description": "Applies multiple changes to a function’s graph to show complex transformations.",
      "difficulty": "advanced"
    },
    {
      "id": "1.8",
      "name": "Arithmetic Operations on Functions",
      "description": "Combines functions by adding, subtracting, multiplying, or dividing them.",
      "difficulty": "intermediate"
    },
    {
      "id": "1.9",
      "name": "Composition of Functions",
      "description": "Applies one function to the result of another to build new functions.",
      "difficulty": "advanced"
    },
    {
      "id": "1.10",
      "name": "One-to-One Functions",
      "description": "A function where each input has a unique output, important for finding inverses.",
      "difficulty": "advanced"
    },
    {
      "id": "1.11",
      "name": "Linear, Quadratic, and Cubic Function Models",
      "description": "Basic function types that model different patterns of change.",
      "difficulty": "basic"
    },
    {
      "id": "1.12",
      "name": "Exponential Models",
      "description": "Functions that model rapid growth or decay, used in real-life applications.",
      "difficulty": "intermediate"
    }
  ],
  "relationships": [
    {
      "source": "1.1",
      "target": "1.2",
      "type": "prerequisite",
      "explanation": "Understanding functions is necessary to define their domain and range."
    },
    {
      "source": "1.2",
      "target": "1.3",
      "type": "related",
      "explanation": "Interval notation is commonly used when expressing domain and range."
    },
    {
      "source": "1.1",
      "target": "1.4",
      "type": "prerequisite",
      "explanation": "You need to understand basic function behavior before classifying them as even or odd."
    },
    {
      "source": "1.1",
      "target": "1.5",
      "type": "prerequisite",
      "explanation": "Understanding functions is key to learning how their graphs shift."
    },
    {
      "source": "1.5",
      "target": "1.6",
      "type": "prerequisite",
      "explanation": "Once shifts are understood, more complex transformations like stretching or reflecting can be learned."
    },
    {
      "source": "1.6",
      "target": "1.7",
      "type": "prerequisite",
      "explanation": "Understanding individual transformations helps in learning combined transformations."
    },
    {
      "source": "1.1",
      "target": "1.8",
      "type": "prerequisite",
      "explanation": "Understanding functions is necessary before performing operations on them."
    },
    {
      "source": "1.8",
      "target": "1.9",
      "type": "prerequisite",
      "explanation": "You need to be comfortable with function operations before learning function composition."
    },
    {
      "source": "1.9",
      "target": "1.10",
      "type": "prerequisite",
      "explanation": "Understanding composition is helpful when studying one-to-one functions and their inverses."
    },
    {
      "source": "1.1",
      "target": "1.11",
      "type": "related",
      "explanation": "Function models are real-world applications of the basic function concept."
    },
    {
      "source": "1.11",
      "target": "1.12",
      "type": "prerequisite",
      "explanation": "Linear, quadratic, and cubic models are usually taught before exponential models."
    }
  ]
}

CONCEPT_DECOMPOSITION_EXAMPLES_2 = {
  "main_concept": "Normal Distribution",
  "Explanation": "A normal distribution is a symmetric, bell-shaped curve where the mean represents the center and the variance measures how spread out the data is. Most data falls close to the mean, especially within a few standard deviations.",
  "sub_concepts": [
    {
      "id": "1.1",
      "name": "Mean of a Normal Distribution",
      "description": "The average value of the data and the center point of the bell curve.",
      "difficulty": "basic"
    },
    {
      "id": "1.2",
      "name": "Variance of a Normal Distribution",
      "description": "A measure of how much the data spreads out from the mean.",
      "difficulty": "intermediate"
    },
    {
      "id": "1.3",
      "name": "Standard Deviation",
      "description": "The square root of variance; it shows the average distance of data from the mean.",
      "difficulty": "intermediate"
    },
    {
      "id": "1.4",
      "name": "Properties of the Normal Distribution",
      "description": "The distribution is symmetric with the mean, median, and mode all equal, forming a bell curve.",
      "difficulty": "basic"
    },
    {
      "id": "1.5",
      "name": "Empirical Rule (68-95-99.7 Rule)",
      "description": "Describes how data is spread in a normal distribution using standard deviations.",
      "difficulty": "intermediate"
    }
  ],
  "relationships": [
    {
      "source": "1.1",
      "target": "1.4",
      "type": "prerequisite",
      "explanation": "Understanding the mean is necessary to grasp the symmetry and central tendency of the normal distribution."
    },
    {
      "source": "1.2",
      "target": "1.3",
      "type": "prerequisite",
      "explanation": "Standard deviation is derived from the variance, so variance must be understood first."
    },
    {
      "source": "1.3",
      "target": "1.5",
      "type": "prerequisite",
      "explanation": "The empirical rule is based on standard deviations, so understanding standard deviation is essential."
    },
    {
      "source": "1.4",
      "target": "1.5",
      "type": "related",
      "explanation": "The empirical rule is one of the defining properties of a normal distribution."
    }
  ]
}